First and foremost, fuck Github. It doesn't define who you are and what you are capable of. Don't buy into it. For reference, my Github is set to private and has a single repository pointing people to my personal site. My personal site has 8 sentences on it. It says who I am and what I've built (software products). I don't blog. I don't share code. What you need is to be able to demonstrate what you are capable of. I…
I do agree that job postings asking for personal projects are a little bit over the top. The main problem with building products is the idea, the spark, honestly I can't see at the moment a product that people need, or even less, a product that I would need
Make a cronjob monitoring service. Make a "privacy focused analytics" platform. Make a session replay service. Make a "javascript error collection" service. Make a user feedback widget as a service.
It doesn't matter what you make. Pick something that has been done before and do it on your own.
If you are hell bent on live streaming-- live streaming that would be far more interesting than watching someone rebuild react.